Radiotherapy is an established treatment modality of cancer where radiation is delivered to the patients from internal or external sources. This thesis explores and introduces improvements to computational methods that are used in the application of internal and external radiotherapy. The summary discusses radiotherapy planning and reviews model-based dose calculation methods in internal and external radiotherapy. Treatment planning methods of internal radionuclide therapy are devloped and applied to analyze radionuclide therapy cases. The thesis also reports on the development of a pencil-beam dose kernel -based calculation method for external photon therapy that also accounts for local variations in tissue material densities in 3D space.

Aalto-D

D 57

/2016

9HSTFMG*aghchi+

ISBN 978-952-60-6727-8 (printed) ISBN 978-952-60-6728-5 (pdf) ISSN-L 1799-4934 ISSN 1799-4934 (printed) ISSN 1799-4942 (pdf) Aalto University School of Science Department of Neuroscience and Biomedical Engineering www.aalto.fi

BUSINESS + ECONOMY ART + DESIGN + ARCHITECTURE SCIENCE + TECHNOLOGY CROSSOVER DOCTORAL DISSERTATIONS

Joakim P

yyry C

onvolution and model-based dose calculation m

ethods in radionuclide and external-beam photon therapy

Aalto

Unive

rsity

2016

Department of Neuroscience and Biomedical Engineering

Convolution and model-based dose calculation methods in radionuclide and external-beam photon therapy

Joakim Pyyry

DOCTORAL DISSERTATIONS

Preface

This project started twenty years ago in the spring of 1996, when my

Thesis advisors Kalevi Kairemo and Mikko Tenhunen recognized a need

to improve treatment planning for radionuclide therapy. At the time, I

was developing a treatment planning system for brachytherapy, and we

started to extend the system to include radionuclide dose calculations. I

am greatly indebted to my advisors for their support, creativity, and drive

that pushed me to move this project forward. I also want express my

gratitude to the patients presented in the case studies and the clinical

staff involved in the patient care and data acquisition.

During my doctoral studies, I have been employed by Varian Medical

Systems Finland Oy (formerly Varian-Dosetek Oy) working in radiother-

apy research and development projects. I want to thank all my colleagues

at Varian for the motivating and inspiring work environment where fight-

ing against cancer is our common goal. Pekka Aalto created a world-class

treatment planning research and development center at Dosetek in Fin-

land, and supported me in many ways during the years. I am grateful to

Ramin Baghaie for the support and encouragement that he gave me to

finalize my doctoral studies, and for his perceptive review and comments

on the manuscript.

I want to thank all the co-authors of the publications and my other

collaborators. Jyrki Alakuijala has been an outstanding mentor induct-

ing me to the process of scientific publication, as well as to the world

of professional software development. The AAA method would not ex-

ist without Waldemar Ulmer’s and Wolfgang Kaissl’s early investigations

and Hannu Helminen’s key contributions during the first implementa-

tion. Since then, numerous people have contributed to the success of the

AAA and its improvements: particularly the members of the VMS Fin-

land Applied Research Department and the large user base of medical

1

Preface

physicists around the world.

At Aalto University, my sincere thanks go to Professor Toivo Katila,

who guided me during the start of my doctoral studies, and to Professor

Lauri Parkkonen who took over the supervision during the final stretch of

my studies. I am grateful to the official pre-examiners, Professor Dietmar

Georg and Dr. Mark Lubberink, for their insightful comments and appro-

priate suggestions. I want to express my gratitude to Raine Vasquez for

his critical language review.

The encouragement and care from my parents Helena and Jorma has

enabled my education and other endeavors in life. Thank you. Olavi and

Ansa, you fill me with joy and keep me energized with your speed of move-

ment and creativity. Finally Noora: without your love, companionship, ex-

emplary passion for scientific writing and encouragement to finalize this

undertaking, it would have taken me yet another twenty years.

Helsinki, March 22, 2016,

Joakim Pyyry

2

Contents

Preface 1

Contents 3

List of Publications 5

Author’s Contribution 7

1. Introduction 11

1.1 Principles of radiotherapy . . . . . . . . . . . . . . . . . . . . 12

1.2 Brachytherapy . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.3 Radionuclide therapy . . . . . . . . . . . . . . . . . . . . . . . 12

1.4 External-beam radiotherapy . . . . . . . . . . . . . . . . . . . 13

1.5 Radiation physics of photons and electrons . . . . . . . . . . 14

1.6 Radiation transport and absorbed dose calculations . . . . . 15

1.7 Aims of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . 17

2. Radiotherapy treatment planning and sources of radiation 19

2.1 Dose calculation in radionuclide therapy . . . . . . . . . . . . 19

2.2 Distribution of activity in radionuclide therapy . . . . . . . . 21

2.3 Treatment machine modeling . . . . . . . . . . . . . . . . . . 23

3. Model-based convolution and superposition methods in ab-

sorbed dose calculation 25

3.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2 Point-spread and kernel methods . . . . . . . . . . . . . . . . 26

3.2.1 Brachytherapy . . . . . . . . . . . . . . . . . . . . . . . 26

3.2.2 Radionuclide therapy . . . . . . . . . . . . . . . . . . . 27

3.2.3 3D kernel methods in external-beam therapy . . . . . 27

3.3 Pencil-beam methods . . . . . . . . . . . . . . . . . . . . . . . 28

3

Contents

3.3.1 Exponential modeling of pencil beams . . . . . . . . . 29

3.3.2 Superposition of pencil beams . . . . . . . . . . . . . . 29

3.3.3 Build-up and build-down correction . . . . . . . . . . 30

3.4 Computational considerations . . . . . . . . . . . . . . . . . . 31

3.4.1 Performance characteristics . . . . . . . . . . . . . . . 31

3.4.2 Parallel computing . . . . . . . . . . . . . . . . . . . . 32

4. Summary of results 35

4.1 Patient-specific distributions in radionuclide therapy . . . . 35

4.2 A pencil beam superposition algorithm in external radio-

therapy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

5. Discussion and conclusions 41

5.1 Overall results . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5.2 Contribution to the field . . . . . . . . . . . . . . . . . . . . . 42

5.3 Future directions . . . . . . . . . . . . . . . . . . . . . . . . . 43

5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

Errata 57

Publications 59

4

List of Publications

This thesis consists of an overview and of the following publications which

are referred to in the text by their Roman numerals.

I J. Laitinen, J. Alakuijala, H. Helminen, S. Sallinen, M. Tenhunen, and

K. Kairemo. Spect-based radioimmunotherapy planning system. In

IEEE Engineering in Medicine and Biology 19th Annual Conference,

Chicago, 781–784, 1997.

II J.O. Laitinen, K.J. Kairemo, A.P. Jekunen, T. Korppi-Tommola, and M.

Tenhunen. The effect of three dimensional activity distribution on the

dose planning of radioimmunotherapy for patients with advanced in-

traperitoneal pseudomyxoma. Cancer 80, 2545–2552, 1997.

III J.O. Laitinen, M. Tenhunen, and K.J. Kairemo. Absorbed dose esti-

mates for I-131 labelled monoclonal antibody therapy in patients with

intraperitoneal pseudomyxoma. Nucl Med Commun 21, 355–360, 2000.

IV J.O. Pyyry, J. Merenmies, M. Tenhunen, M. Heikinheimo, K. Parto,

M. Arola,K. Rönnholm, H. Isoniemi, R. Karikoski, E.L. Kamarainen,

M. Seppänen,J. Heikkonen, F. Augensen, W.H. Wegener, D.M. Golden-

berg, and K.J. Kairemo . Radioimmunotherapy for recurrent childhood

hepatoblastoma after liver transplantation. World Journal of Nuclear

Medicine 7, 146–157, 2008.

V W. Ulmer, J. Pyyry, and W. Kaissl. A 3D photon superposition/convolution

algorithm and its foundation on results of Monte Carlo calculations.

5

List of Publications

Physics in Medicine and Biology 50, 1767–1790, 2005.

VI L. Tillikainen, H. Helminen, T. Torsti, S. Siljamäki, J. Alakuijala, J.

Pyyry, and W. Ulmer. A 3D pencil-beam-based superposition algorithm

for photon dose calculation in heterogeneous media. Physics in Medicine

and Biology 53, 3821–3839, 2008.

6

Author’s Contribution

Publication I: “Spect-based radioimmunotherapy planning system”

The author (J. Laitinen) implemented the dose-kernel-based dose calcula-

tion algorithm and dose visualization system and integrated the methods

into an existing brachytherapy treatment planning system. The author

was solely responsible of the production of the manuscript.

Publication II: “The effect of three dimensional activity distributionon the dose planning of radioimmunotherapy for patients withadvanced intraperitoneal pseudomyxoma”

The author (J. Laitinen) developed and utilized a radiotherapy planning

system to register images and calculate doses. The author analyzed the

results and was primarily responsible of the writing and revision of manuscript.

Publication III: “Absorbed dose estimates for I-131 labelledmonoclonal antibody therapy in patients with intraperitonealpseudomyxoma”

The author (J. Laitinen) utilized the developed radiotherapy planning sys-

tem and MIRD methodology to analyze radiation doses in patients receiv-

ing radioimmunotherapy. The author was primarily responsible of the

production of the manuscript.

7

Author’s Contribution

Publication IV: “Radioimmunotherapy for recurrent childhoodhepatoblastoma after liver transplantation”

The author constructed the dose kernels for In-111 and Y-90 and analyzed

the radiation doses utilizing the developed software employing automatic

image registration and point-dose-kernel dose calculation. The author

was jointly responsible for the production of the manuscript contributing

to the absorbed dose calculation section and to the methods related to dose

calculations and image registration.

Publication V: “A 3D photon superposition/convolution algorithmand its foundation on results of Monte Carlo calculations”

The author participated in developing the methods and verification of the

implementation of the methods. The author analyzed the radiation doses

utilizing the developed software and co-ordinated experimental verifica-

tion of the methods. The author assisted in the production and review of

the manuscript.

Publication VI: “A 3D pencil-beam-based superposition algorithmfor photon dose calculation in heterogeneous media”

The author participated in developing the methods related to the expo-

nential basis functions and scaling for tissue heterogeneities. The au-

thor had a minor role in assisting in the production and review of the

manuscript. This article was also part of the PhD thesis of Tillikainen

(2009).

8

Abbreviations and Symbols

A Activity distribution

e Electron radiation

E Energy

Φ Angular fluence

γ Photon radiation

h Pencil-beam dose kernel

k Point-dose kernel

λ Distance from the central axis

~p Spatial position co-ordinate (px, py, pz)

µ Attenuation co-efficient

N Number of elements

Ω Direction

~r Spatial position

ρ Density

σ Total cross section

SR Radiative stopping power

T TERMA — Total energy released in the material

3D Three dimensional

AAA Analytical anisotropic algorithm

CAX Central axis

9

Abbreviations and Symbols

CCC Collapsed cone convolution

CPU Central processing unit (of a computer)

CT Computed tomography

FFT (Discrete) fast Fourier transform

GPU Graphics processing unit

IMRT Intensity modulated radiotherapy

ICRU International commission on radiation units and measurements

MIRD Committee on medical internal radiation dose

MC Monte Carlo

MoAb Monoclonal antibody

MR Magnetic resonance

MSM Multiple source models

OLINDA Organ level internal dose assessment

PB Pencil beam

PET Positron emission tomography

QA Quality assurance

SBRT Stereotactic body radiation therapy

SC Superposition/convolution

S-factor Specific absorbed dose factor in MIRD methodology

SPECT Single-photon emission computed tomography

TERMA Total energy released in the material

TPS Treatment planning system

VMAT Volumetric modulated arc therapy

VOI Volume of interest

10

1. Introduction

Cancer is a malignant disease which is among the leading causes of mor-

tality in the world, with approximately 14 million new cases annually in

2012 leading to 8.2 million deaths, according to World Health Organiza-

tion. Cancer incidences rise with aging of the population, and it is esti-

mated that there will be 70% more cancer cases within next two decades.

(WHO 2015)

Cancer is a generic term for a group of diseases. The defining feature

of cancer is the rapid growth of abnormal cells that spread to other organs

by invading adjoining parts of the body or through circulation referred to

as metastasizing. Metastases cause the majority of deaths from cancer.

Every cancer type requires a tailored approach to treatment. Treat-

ment regimens include multiple modalities: surgery, radiotherapy, and

chemotherapy. The different modalities are often used in combination.

The goal of the treatment is to cure cancer or to prolong life, in addition to

improving the patient’s quality of life. Radiotherapy is a key component

of comprehensive cancer care, but worldwide access to it is low. As Atun

et al. (2015) point out there are considerable benefits to further develop

radiotherapy and scale it up worldwide.

This Thesis explores and introduces improvements to computational

methods that are used in the application of radiotherapy. These meth-

ods are routinely used in clinical radiotherapy practice and fall under the

domain of computational physics. The methods are very relevant as they

provide an optimal balance of accuracy and speed in the everyday practice

of radiotherapy.

11

Introduction

1.1 Principles of radiotherapy

Radiotherapy refers to the utilization of ionizing radiation for a therapeu-

tic effect, typically for cancer treatment; for a comprehensive overview of

the subject see e.g. Halperin et al. (2008). Radiation is delivered either ex-

ternally, from outside the body, or internally. Internal therapy is further

divided to brachytherapy and radionuclide therapy. In brachytherapy, a

radioactive source is placed in or near the tumor; in radionuclide therapy,

the radioactive isotopes are delivered systemically inside the body.

Ionizing radiation causes damage in cells, with increased damage by

the amount of energy deposited by the ionizing radiation in the tissue.

Both normal tissue and cancer cells are affected but exhibit different cell-

survival probability for the same radiation dose level. Many cancer cells

are more sensitive to radiation than healthy tissue due to the reduced

efficacy of the biochemical repair processes of the damaged cell nuclei un-

dergoing reproduction (due to the growth of the cancer). In addition, the

ability to focus the radiation for a higher dose in the tumor compared to

normal tissue allows for improved therapeutic ratio.

1.2 Brachytherapy

Brachytherapy is a form of radiotherapy where sealed radioactive sources

are placed in the vicinity of the treated tumor. Typically it is applied

internally via cavities or interstitially with needles. It is oldest form of

radiotherapy as it was first applied in 1901 shortly after the discovery of

radioactivity. Low dose rate delivery typically can involve permanent im-

plants of sealed sources or temporary application of radioactive sources

for several hours. Shorter high dose rate treatments are typically per-

formed with afterloading devices where the radioactive source is moved

in and out off the treatment region using remote control.

1.3 Radionuclide therapy

Radionuclide therapy is an internal radiotherapy technique which relies

on certain biological mechanisms to provide a higher concentration of ra-

dionuclides in the vicinity of cancerous cells in order to produce a higher

radiation dose. Often radionuclide therapy relies on radiolabeled car-

riers like liposomes, antibodies, or nano-particles to localize in tumors

12

Introduction

(Williams et al. 2008). The radionuclides are administered systemically

via circulation, or into cavities.

The radionuclides that are useful for therapy undergo three modes of

decay: beta, alpha, and electron capture or isomeric transition by emis-

sion of Auger and Coster-Kronig electrons. Selection criteria, in addition

to the mode of decay, include energy of released particles, chemical prop-

erties, production methods, as well as biological behavior (Zweit 1996).

Similarly to other modes of radiotherapy — knowledge of the absorbed

radiation dose is needed to assess the toxicity and efficacy of radionuclide

therapy. The absorbed dose is a macroscopic concept, but for radionuclide

therapy microdosimetry — study of radiation energy deposition in micro-

scopic volumes — may be indicated for low-energy auger-emitters (Humm

et al. 1993). The notion of biological effective dose has been introduced to

take into account the biological effects various dose rates and different

types of radiation. The aspects of radiobiology can be utilized in radionu-

clide therapy in order to estimate the best dose for tumor control, while

protecting the healthy tissues (Pouget et al. 2015).

1.4 External-beam radiotherapy

External-beam radiotherapy is a mode of radiation treatment where the

radiation originates from sources externalto the body. The radiation types

used are photons, electrons, or heavier charged particles. The most com-

mon is photon therapy using megavoltage brehmsstrahlung x-rays gener-

ated by linear electron accelerators. Photon beams can also be generated

with a radioactive source such as cobalt-60. Charged-particle therapy has

its own role in cancer management but is not discussed in the Thesis.

The external beam is directed from outside the body to the site of the

treatment target (tumor). In order to ensure a conformal and high radi-

ation dose inside the target, the radiation needs to be focused from mul-

tiple directions to the common target. The beam intensity and shape are

typically produced by a computer-controlled multi-leaf collimation device

integral to the treatment delivery system.

13

Introduction

1.5 Radiation physics of photons and electrons

Photon radiation interacts with matter and deposits energy via complex

interaction cascades. When photons interact with material, the primary

photon is absorbed in the interaction. A secondary photon is re-emitted in

a scattering (coherent or incoherent) interaction. The scattering process is

similar to a change in the direction and energy of the photon; this change

occurs through absorption and emission of photons. In the process, elec-

trons are also ejected from the interacting atoms or they are created as

electron — positron pairs. The main interactions of photons with atoms

are called photoelectric absorption, Rayleigh (coherent) scattering, Comp-

ton (incoherent) scattering, and electron — positron pair production. The

relative importance of various interactions varies with photon energy and

the medium. The total mass attenuation coeffiecients have been tabu-

lated extensively by Hubbell and Seltzer (1996) and Figure 1.1 shows an

example of photon attenuation factors as function energy.

Figure 1.1. Photon attenuation is plotted separately for each interaction type with the to-tal mass attenuation factor as a function of energy in iron medium (Tuszynski2010).

In photon radiotherapy, electrons are generated in the interactions of

the photons with matter. These electrons interact intensively with mat-

ter. Electrons interacting with the orbital electrons of the atoms create

secondary electrons and lose part of their initial energy. Photons are cre-

ated when the electrons interact with the Coloumb field of the nucleus

of the atom in a process called brehmsstrahlung. The electromagnetic

interactions couple the electrons and photons into a combined shower of

particles which makes the modeling of the phenomenon complicated.

14

Introduction

1.6 Radiation transport and absorbed dose calculations

The radiation transport problem can be described as a linear differential

equation that takes the form of the Boltzmann transport equation origi-

nally formulated by Ludwig Boltzmann to describe the statistical behav-

ior of a thermodynamic system not in a thermodynamic equilibrium. The

transport equation can be solved by numerical grid-based methods, as has

been demonstrated in the radiotherapy domain by several groups (Kotilu-

oto et al. 2007; Vassiliev et al. 2010). However, the historically more im-

portant method in the field of radiotherapy has been the stochastic Monte

Carlo (MC) solution to the Boltzmann transport equation (Andreo 1991;

Rogers 2006). There have been several practical implementations where

speed and accuracy have been optimized for routine clinical use (Neuen-

schwander et al. 1995; Fippel et al. 1997; Fippel et al. 1999; Kawrakow

and Fippel 2000; Fix et al. 2010).

The Boltzmann equation for transport of photons (γ) can be written as

Ω · ~∇Φγ + σγt Φγ = qγ + qγγ (1.1)

and for electrons (e) the Boltzmann-Fokker-Planck transport equation as

Ω · ~∇Φe + σetΦe − ∂

∂E(SRΦe) = qe + qee + qγe (1.2)

where Φ(~r,E, Ω) describes the angular fluence for photons and electrons

and is a function of spatial position (~r), energy (E) and direction (Ω).

The macroscopic total cross sections for photons is σγt and for electrons

σet . SR(~r,E) is the combined restricted collisional and radiative stopping

power. The scattering source terms can be written in the integral form as

qγγ(~r,E, Ω) =

∫ ∞

0dE′

∫

4π

σγγt (~r,E′ → E, Ω · Ω′)Φ(~r,E, Ω)dΩ′ (1.3)

qγe(~r,E, Ω) =

∫ ∞

0dE′

∫

4π

σγet (~r,E′ → E, Ω · Ω′)Φ(~r,E, Ω)dΩ′ (1.4)

qee(~r,E, Ω) =

∫ ∞

0dE′

∫

4π

σeet (~r,E′ → E, Ω · Ω′)e(~r,E, Ω)dΩ′, (1.5)

where qγγ is the photon source resulting from photon interactions, qγe

is the electron source resulting from photon interactions and qee is the

electron source resulting from electron interactions. The corresponding

macroscopic differential cross sections are σγγt , σγet , σeet for photon–photon,

photon–electron, and electron–electron interactions respectively. The

15

Introduction

above equations are somewhat simplified in the interactions such that

photons can produce electrons but electrons do not produce photons. Addi-

tionally, the pair-production particles are assumed to be electrons (instead

of an electron–positron pair). Additionally, the electrons are transported

with a continuous slowing down approximation. In the radiotherapy do-

main, these simplifications are not affecting the accuracy of the solution

(Vassiliev et al. 2010).

The solution of the transport equation allows for an accurate deter-

mination of the absorbed energy in the material including the relevant

physics. As reviewed earlier, photons are indirectly ionizing particles and

do not deposit significant energy, but through interaction with medium

they transfer their energy to electrons and positrons that ionize and trans-

fer their energy until it is exhausted. The energy absorbed can be further

converted into absorbed dose which is strictly defined as mean energy im-

parted (by ionizing radiation) per mass (ICRU 1988).

In this Thesis methods that directly solve the transport equation are

not utilized but rather other methods to calculate the absorbed dose are

employed. These methods are typically phenomenological models or math-

ematical constructs that separate the effects of scattered radiation from

the primary radiation such as the Superposition/convolution (SC) algo-

rithm and are reviewed further in Chapter 3.

16

Introduction

1.7 Aims of the Thesis

The aims of this Thesis are summarized in the Table 1.1 below. The meth-

ods developed in this Thesis are to provide the basis for accurate and

fast absorbed dose calculations in the external-beam radiotherapy and

radionuclide therapy, and are to be applied in analysis of radionuclide

treatments.

Table 1.1. Aims of the Thesis

Aim Publication

1. To develop a general methodology for three dimen-

sional (3D) treatment planning of radionuclide therapy

I, II

2. To apply convolution (dose-kernel) methods in ra-

dionuclide therapy treatment planning in order to com-

pare a patient-specific dose calculation method with the

widely used Committee on medical internal radiation

dose (MIRD) S-factor model for patients receiving ra-

dionuclide therapy.

II, III, IV

3. To develop a Pencil-beam (PB) dose-kernel-based cal-

culation method for external photon therapy that also

accounts for local variations in tissue material densities

in 3D space.

V, VI

17

Introduction

18

2. Radiotherapy treatment planning andsources of radiation

The overall radiotherapy treatment planning process aims to model the

treatment outcome. Current practice is to calculate and analyze radia-

tion dose as a surrogate for biological effectiveness of the treatment. The

overall process is depicted in Figure 2.1. The process is similar for ra-

dionuclide and external-beam therapy. The main difference is the patient-

specific radionuclide imaging that is used to construct the radiation source

model in radionuclide therapy, whereas in external-beam therapy the

source modeling is independent of the patient.

The treatment planning process starts with acquisition of anatomical

images used for anatomy modeling and dose calculation. X-ray Computed

tomography (CT) is suitable for dose calculation purposes due to its ge-

ometrical accuracy and ability to provide density and material composi-

tion data. Magnetic resonance (MR) imaging provides great soft tissue

contrast and is very useful for determining the boundaries of critical or-

gans and extent of macroscopic tumor growth. Anatomy modeling is done

by manually or semi-automatically segmenting the image data, providing

geometrical models of the patient’s anatomy. Dose calculation uses the

source model and an algorithm to solve the radiation transport problem

in the patient-specific geometry. The resulting dose distribution is visu-

alized and analyzed utilizing e.g. dose volume histograms (Drzymala et

al. 1991). A computer implementation of the radiotherapy process and

methods is called a Treatment planning system (TPS).

2.1 Dose calculation in radionuclide therapy

The absorbed dose in radionuclide therapy has commonly been calculated

using biokinetic data from a diagnostic tracer study, using a method de-

veloped by the MIRD (Watson et al. 1993). The traditional MIRD method

19

Radiotherapy treatment planning and sources of radiation

Acquire Images

Model Anatomy Calculate Dose

Model Source

Analyze & Visualize

SPECT

Acquire Images

Model Anatomy Calculate Dose

Model Source

Analyze & Visualize

CT, MR

a) b)

CT, MR

Figure 2.1. The treatment planning process for a) radionuclide therapy and b) external-beam radiotherapy are very similar.

includes a model patient phantom where various organ-to-organ contri-

butions of dose have been pre-calculated with the MC method to solve the

above transport equations. When applied in a clinical setting, the MIRD

method fails to include patient-specific anatomy and non-homogenous dis-

tribution of the radionuclide inside a given organ. A computer implemen-

tation of the methodology that is currently widely used is called Organ

level internal dose assessment (OLINDA) (Stabin et al. 2005).

Various authors have studied methods that overcome these limitations.

Although Traino et al. (2013) report on a simplified patient-specific method

based on the MIRD S-factors, the most common solution is to calculate the

absorbed dose distributions using a point-source-kernel approach with

patient-specific activity maps (Sgouros et al. 1990; Sgouros et al. 1993;

Erdi et al. 1994; Kolbert et al. 1997; Giap et al. 1995b; Giap et al. 1995a;

Erdi et al. 1998; Gardin et al. 2003; Guy et al. 2003; Loudos et al. 2009).

This method is also utilized in papers I, II, III and IV. Another approach

is to utilize the so called voxel S-factors to calculate patient-specific dose

estimates in combination with point kernels as described by Jackson et

al. (2013). As in external-beam radiotherapy, MC calculations have also

been proposed and applied in radionuclide therapy for patient-specific

dose calculations by Tagesson et al. (1996) and Furhang et al. (1996a)

and Furhang et al. (1997) and more recently applied e.g. by Ljungberg

et al. (2002), Chiavassa et al. (2005), Prideaux et al. (2007), Marcatili et

al. (2013), and Grimes and Celler (2014). Dieudonné et al. (2013) has

compared accuracy between the dose kernel methods and MC methods.

20

Radiotherapy treatment planning and sources of radiation

2.2 Distribution of activity in radionuclide therapy

Overall treatment planning and dosimetry of radionuclide therapy re-

quires an estimation of the radionuclide activity distribution in the pa-

tient over time (Strand et al. 1993b; Sgouros et al. 1990). This cumulative

activity distribution can be derived form nuclear medical imaging tech-

niques (planar gamma camera, Positron emission tomography (PET), and

Single-photon emission computed tomography (SPECT)) and pharmacoki-

netic data. The image data has to be quantified so that absolute activity

counts needed for cumulative activity distribution can be obtained. Ad-

ditionally, pharmacokinetic modeling complements the estimation of cu-

mulated activity in the image. The basic pharmacokinetic modeling of

radiolabeled Monoclonal antibody (MoAb) has been reviewed by Strand et

al. (1993a) and a software package to calculate cumulated activities has

recently been developed by Kletting et al. (2013).

The general goal for emission-computed tomography is to be able to

quantitatively determine localization volumes and measurement of activ-

ities in small and large tumors. There are various factors that affect the

accuracy of the quantification of emission-computed images. In SPECT,

the most important physical factors are scatter and attenuation correc-

tions, limited spatial and energy resolutions of gamma cameras, septal

penetration of high energy photons, and statistical noise of low count

densities. The system resolution is about 9 mm and full-width-at-half-

maximum of SPECT devices range from 7 - 18 mm, which leads to partial

volume effects i.e. loss of apparent activity within small objects (Erlands-

son et al. 2012). The use of PET would provide improved spatial resolution

and quantification. For PET systems, the spatial resolution is about 6 -

13 mm. The limitations of PET has been the availability of the technology

and problems associated with short lived radionuclides. Lubberink et al.

(1999) and Lundqvist et al. (1999) discuss the use of PET for radionuclide

quantification and dosimetry.

For treatment planning purposes, the imaging can be done prior to

therapy or during therapy to verify estimate actual dose delivered, and

both methods where used in II, III and IV. The pre-therapy imaging can

be carried out using an appropriate radionuclide label for the targeting

agent with a gamma camera or positron camera. The pre-therapy forms

the basis of targeted radionuclide therapy planning. Therapy imaging is

more demanding but is essential for confirming the information provided

21

Radiotherapy treatment planning and sources of radiation

by pre-therapy planning study.

The information that is crucial to dosimetry is tracer concentration at

several time points throughout the residence time of the tracer. The im-

ages need to be corrected for detector uniformity of response and dead-

time, photon attenuation and scattering effects (Ott 1996). The conver-

sion of image data in counts per voxel to concentration requires calibra-

tion data of phantoms imaged with known radioactive concentration of

tracer. The accuracy of the kinetics of the radionuclide concentration is

furthermore restricted by the temporal sparseness imaging data.

The kinetics of the therapeutic dose may vary from the tracer dose.

Although the pre-therapy dosimetry is important in the guidance of the

treatment, the actual dose delivered in treatment needs to be determined

using on-therapy imaging. The estimation of doses in III and IV where

done based on on-therapy SPECT images and quantification using planar

gamma camera images with a standard source as a reference.

Obtaining qualitative data of activity distributions from SPECT re-

quires careful methods in acquiring and processing the data (Ott 1996;

Leichner et al. 1993; Dewaraja et al. 2012). Quantitative planar and

SPECT images can be obtained by using attenuation and scatter correc-

tion methods. Hutton et al. (2011) have produced a recent review of the

current scatter correction methods and notes that the most widely used

ones are the scatter subtraction by multiple energy window approaches,

as described by Macey et al. (1995). Ljungberg et al. (1994) have com-

pared a few different methods and concluded that there is no significant

difference in quantification accuracy between them.

Improved reconstruction accuracy using iterative methods is an active

research area (see e.g. (Beekman et al. 2002; Ouyang et al. 2007)). An

application of such methods in radionuclide therapy with absorbed dose

estimation has been reported by Cheng et al. (2014). The emerging hy-

brid SPECT/CT and PET/CT devices are also aiding in better reconstruc-

tion and image processing methods for quantitative imaging by providing

complementary information about the attenuation properties of the pa-

tient (Cade et al. 2013). It is essential to validate the methodology used

to extract quantitative information from reconstructed images because

different devices and reconstruction algorithms have a big effect on the

quality of the images.

22

Radiotherapy treatment planning and sources of radiation

2.3 Treatment machine modeling

In order to characterize the energy fluence output of a linear accelera-

tor suitable for transport equation solvers or model-based SC and Pencil

beam (PB) algorithms, one needs a physical source model of the treatment

machine. The output of a treatment machine is well understood thanks

to the extensive study of radiation output based on the geometrical con-

struction (of the machine) by utilizing the MC method — see e.g. Mohan

et al. (1985), Ma et al. (1999), Sheikh-Bagheri and Rogers (2002b) and

Sheikh-Bagheri and Rogers (2002a) using MC based tools like BEAM as

described by Rogers et al. (1995).

For practical application, simplified models have been developed that

divide the main sources of radiation into several components that can be

described by a small set of model parameters. These are called Multiple

source models (MSM) and have been developed by various independent

researchers like Liu et al. (1997), Fix et al. (2001b), Deng et al. (2004),

Fippel et al. (2003), Fix et al. (2004), and Tillikainen et al. (2007) for the

purposes of dose calculations. Another use for simplified source models

is in Quality assurance (QA), where independent monitor unit calcula-

tions can be performed with simplified energy fluence models (Georg et

al. 2007).

Typical MSM models include a point source for primary radiation from

the bremsstrahlung target and finite size sources to account for extra-

focal radiation from flattening filter, primary collimators, and secondary

jaws. The models also include treatment of the electrons escaping the

linear accelerator in addition to the photon sources. Figure 2.2 shows

schematically a two source photon model with the target and flattening

filter showing in red as the effective photon sources; in addition, electrons

are generated in air by the photon radiation. Some of the models are de-

rived from MC simulation data tuned to match a given linear accelerator,

which is a very time consuming process (Ojala 2014). A more practical

approach is to fit model parameters to a set of measurements for a given

treatment unit in an automated fashion as described by Tillikainen et al.

(2007).

Various photon beam dose models are reported to reproduce dose calcu-

lation results in water within 1-2% accuracy (Jiang et al. 2001; Fix et al.

2001a). Ahnesjö et al. (2005) report the performance of their MSM for a

large number of clinical linear accelerators in which 87% machines can

23

Radiotherapy treatment planning and sources of radiation

Figure 2.2. A schematic drawing of a medical linear accelerator as the radiation sourcein external-beam radiotherapy.

be modeled within 2.5% maximum error. The final element of the model-

ing of the output of a linear accelerator is the back-scatter to the monitor

chamber (Verhaegen et al. 2000; Jiang et al. 2001). The back scatter effect

can be included as a correction factor or as a more comprehensive model

like that described by Liu et al. (2000). The overall accuracy of dose calcu-

lation approach determined both by the accuracy of the source model and

the radiation transport in the patient geometry is discussed in the next

section.

24

3. Model-based convolution andsuperposition methods in absorbeddose calculation

3.1 Background

Widely used model-based dose calculation methods are SC and PB algo-

rithms. The models in these algorithms separate the handling of the pri-

mary photons from the scattered photons, and later combine the effects of

scattered radiation by distributing this in a large volume. The underlying

physics can be utilized to calculate the model parameters, or the parame-

ters can be obtained by fitting the model to measurements. Although both

algorithms separate the primary radiation from the scattered radiation,

they differ in how the separation is done.

In the SC method, the scatter is modeled as a point-spread kernel —

as a Three dimensional (3D) kernel for a given point in the interacting

matter — whereas, in the PB method, the scatter is modeled as a planar

(2D) depth-dependent kernel that is distributed perpendicularly to the

ray lines of the primary radiation from a external point source. Figure

3.1 illustrates the different view points of the a) PB and b) SC algorithms.

The PB method views dose deposited from a small narrow beam with a

varying shape at each depth that includes all effects from upstream scat-

tering events and utilizes this to compose broad beam distributions. The

SC method looks at an unidirectionally moving single photon always in-

teracting at the same point and producing a point-dose-spread kernel that

is used in an macroscopic situation.

The case c) shows kernel of radiation dose of a single point source which

is utilized for internal radiotherapy (brachytherapy or radionuclide ther-

apy), where radiation can be modeled as point sources inside the Volume

of interest (VOI). This method is different from the two others as no sep-

aration of scattered dose is attempted, rather the dose kernel includes all

25

Model-based convolution and superposition methods in absorbed dose calculation

effects of a single point source depositing dose by interactions with the

matter.

a) b) c)

Figure 3.1. Different kernel-based methods have different geometrical separation of thesource term (primary) and the scattered radiation dose. The kernels from leftto right a) PB kernel b) a point-spread kernel and c) point source dose kernel.

3.2 Point-spread and kernel methods

3.2.1 Brachytherapy

The most widely used method to calculate absorbed dose around brachy-

therapy sources are based on the formalism and data from the AAPM

Task Group 43 recommendations (Rivard et al. 2004; Nath et al. 1995).

The method allows inclusion of the effects of the anisotropic distribution

around linear sealed radioactive sources. The method provides absorbed

dose distribution in water medium. The effect of medium heterogene-

ity can be included using transport equation solvers (Poon et al. 2008;

Zourari et al. 2010; Lemaréchal et al. 2015) or by applying the SC method

for brachytherapy as investigated by Carlsson and Ahnesjö (2000b) and

Carlsson and Ahnesjö (2000a). The more accurate methods are especially

useful in the context of improving dose calculation results in the pres-

ence of radiation shields (Tedgren and Ahnesjö 2003; Petrokokkinos et al.

2011).

26

Model-based convolution and superposition methods in absorbed dose calculation

3.2.2 Radionuclide therapy

As discussed earlier, the point-source-kernel approach can provide patient-

specific dose calculations in radionuclide therapy by using an activity map

of the distribution of the radionuclide as input. Absorbed dose distribu-

tion D(~r) at point ~r of known cumulative activity distribution A(~r) in a

homogenous medium can be calculated with a convolution integral (Giap

et al. 1995b):

D(~r) =

∫

V ′A(~r ′)k(|~r − ~r ′|)dV ′, (3.1)

where k(r) is a point source dose kernel (i.e. a spherically symmetric dose

distribution of point source of unit cumulative activity, see 3.1 c)). The

kernels can be obtained from MC simulations, analytical calculations, or

physical measurements. Dose kernels have been constructed using the

MC method, for instance by Furhang et al. (1996b) and Reiner et al.

(2009), or from cross sectional material data by Leichner (1994).

The convolution integral is effectively computed discretely using the

(Discrete) fast Fourier transform (FFT) as investigated by various au-

thors, both in the realm of brachytherapy and radionuclide therapy dose

calculations (Boyer and Mok 1986a; Giap et al. 1995b). The 3D kernel

and the 3D activity map are transformed into the Fourier space, where

the convolution is calculated by multiplication and transformed back to

the spatial domain using an inverse FFT providing the solution to the

convolution integral.

3.2.3 3D kernel methods in external-beam therapy

As discussed earlier, in external-beam therapy the 3D dose kernel has a

different meaning compared to internal therapy. Here, the 3D kernel is

a cumulative dose-spread array of photons interacting in a single point

in the medium. It includes all the effects of photon and electron scatter

interactions leading to adsorbed energy (radiation dose) in the medium.

These dose-spread arrays can be calculated and tabulated by using the

MC method, see Mackie et al. (1988).

The kernel methods rely on the fact that the broad beam dose can be

composed of multiple point irradiations that cause a response that can be

summed up over the whole problem (superposition). The attenuation of

incident photons interacting in the medium is calculated and the Total

energy released in the material (TERMA) is determined. The transport of

energy by scattered photons and electrons is described by the point-spread

27

Model-based convolution and superposition methods in absorbed dose calculation

kernel. The dose distribution is the superposition of the kernels, weighted

by the magnitude of the TERMA impulse for all interaction sites. These

methods were actively developed for the radiotherapy treatment planning

calculations in mid 1980s by several independent groups, as reported by

Mackie et al. (1985), Boyer and Mok (1986b), Boyer and Mok (1985), and

Boyer et al. (1989), Mohan and Chui (1987) and Ahnesjö et al. (1987).

In the most simplest geometries (homogenous materials and simplified

source models), the kernels are spatially invariant, making the superpo-

sition a convolution integral similar to Equation 3.1 where the activity

term A(~r ′) is replaced by TERMA T (~r ′). In this case, this can be very

effieciently computed with the FFT method and was studied by various

authors like Boyer and Mok (1985), Boyer et al. (1989), and Mohan and

Chui (1987). Boyer (1984) and Boyer and Mok (1986b) have extended the

methods for heterogeneous materials by separating kernels into single

and multiple scattering events and applying first order approximations.

The basis of the approximations were developed further by Wong et al.

(1996). The more elaborate treatment of heterogeneity is to scale kernels

by ray-tracing methods, which has become the more prevalent method. A

computationally effective method for the density-scaling is to utilize spa-

tial discretization of the scattering angle and parametrization of scatter

kernels with exponential basis functions, as employed by Ahnesjö (1989)

in his Collapsed cone convolution (CCC) algorithm.

3.3 Pencil-beam methods

The specifics of PB methods as described in VI and V are summarized in

this section. The overview here is compressed and more details can be

found in the original papers. The algorithm has also been commercially

released as the Analytical anisotropic algorithm (AAA) in EclipseTM TPS.

The heterogeneity correction applied in this method is also analogous to

ray-tracing methods used in the 3D SC algorithms.

A PB kernel is a function produced by a narrow beam of monoenergetic

photons of energy E, impinging on a semi-infinite perpendicular water

phantom as depicted in Figure 3.1 a). The polyenergetic PB kernel func-

tion is hβ(z, r), where z and r represent the distance from the surface and

the orthogonal distance from the central axis, respectively. The kernels

hβ(z, r) can been obtained from MC simulations (Ahnesjö et al. 1992) or

deconvolutions from measurements, as described by Storchi and Woud-

28

Model-based convolution and superposition methods in absorbed dose calculation

stra (1996) and Storchi et al. (1999).

3.3.1 Exponential modeling of pencil beams

The methods described in V and VI assume that the pencil beam can be

separated into depth-directed and lateral components. The depth-directed

component accounts for the total energy deposited by the pencil beam for

each layer pz in the calculation grid:

Iβ(pz) = Φβ

∫ ∫hβ(t, υ, pz) dt dυ, (3.2)

where Φβ is the primary energy fluence for the beamlet β.

Lateral dose deposition is modeled as a sum of N radial exponential

functions both in VI and Ahnesjö et al. (1992), whereas in V the lateral

shape is modeled as Gaussian functions. The kernel is separated into sec-

tors at angle θ as the fraction of energy deposited onto an infinitesimally

small angular sector at distance λ from the beamlet central axis. The an-

gular sectors allow for the heterogeneity correction in the lateral direction

by ray-tracing along the discrete rays that represent the collapsed sec-

tors. Given a number N of exponential function components (defined by

coefficients µi), the exponential representation of the lateral pencil-beam

component for a given depth plane pz is of the form

kβ(θ, λ, pz) =N∑

i=1

ci(θ, pz)1

µie−µiλ, (3.3)

where the attenuation coefficients µi are the same for all planes to allow

an efficient computer implementation. The weight parameters ci(θ, pz)

are fitted to the underlying PB kernel data obtained from MC simulations.

The parameter N is chosen to balance between speed and accuracy, and

in the implementation in VI we use the value N = 6.

3.3.2 Superposition of pencil beams

In a homogeneous water, the energy Eβ(~p) deposited from a pencil-beam

beamlet β into a point ~p is the product of the energy deposited on the

calculation plane (Iβ) and the corresponding lateral scatter kernel (kβ). A

factor of 1/λ is also included for normalization:

Eβ(~p) = Iβ(pz)1

λkβ(θ, λ, pz), (3.4)

To account for heterogenous material, the density-scaling approxima-

tion where each spatial dimension of the scatter process is scaled locally

29

Model-based convolution and superposition methods in absorbed dose calculation

by the inverse relative electron density 1/ρw can be used:

ρw(~p) := ρelec(~p)/ρelecwater, (3.5)

where ρelec is the local electron density at point ~p and ρelecwater the electron

density of water. It is necessary to account for the effective (radiological)

distance deff(X) =∫X ρw(~p)d~p for an arbitrary path X.

The scaling of the lateral scatter kernel is done by calculating the ra-

diological path length in a radial manner from the center of the pencil

beam. Then the heterogeneity-corrected lateral kernel k′β(θ, λ, pz) is given

by

k′β(θ, λ, pz) = kβ(θ,p′zpzλ′, p′z)ρw(~p), (3.6)

where λ′ is the effective radius computed as λ′ = deff(Cβ(θ, pz)). This radi-

ological pathlength scaling method based on electron density is a common

approach to account for tissue heterogeneities in kernel based models,

as reported in the review by Ahnesjö and Aspradakis (1999), and has

been found to be more appropriate than the scaling based on mass den-

sity by Seco and Evans (2006).

The I function also needs to be scaled for heterogeneities by expressing

it in terms of effective depth p′z. Thus, the heterogeneity corrected depth-

directed component I ′β is calculated as

I ′β(pz) = Iβ(p′z)ρw( ~pβ), (3.7)

where ~pβ is the point on the pencil-beam central axis at depth pz, p′z is the

effective depth given by deff(Pβ), where Pβ is the path from pencil-beam

entry point to ~pβ.

The heterogeneity-corrected energy distribution from a single beamlet

β is then calculated as:

Eβ(~p) = I ′β(pz)1

λk′β(θ, λ, pz). (3.8)

The total deposited energy into a grid point ~p is then simply an integral

of contribution of all the individual beamlets over the broad beam area:

Etot(~p) =

∫ ∫

β′Eβ′(~p) dβ′. (3.9)

3.3.3 Build-up and build-down correction

The separation of the heterogeneity correction into two components, the

depth-directed component in (3.7) and the lateral scatter component in

30

Model-based convolution and superposition methods in absorbed dose calculation

(3.6) is clearly an approximation, but it produces good results after suf-

ficient distance from the material interface in slab-like phantoms. How-

ever, near the interfaces it fails to reproduce the gradual build-up and

build-down effects — instead, the dose would jump abruptly to a new

equilibrium level. This is caused by the fact that the scattered particles

originating before the interface are not correctly taken into account by

this method.

The size of the build-up or build-down transition is determined by the

mean range of the scattered particles. Also, the dominant scatter com-

ponent in a therapeutic radiation beam is forward-directed. Thus to re-

produce these effects using a pencil-beam based model, it is not sufficient

to scale the pencil beam in its entirety by the effective distance, but a

method to account for the forward-directed energy shift is needed.

The technique chosen in this work is to employ a forward build-up con-

volution kernel to the energy deposition introduced in V and refined in

VI using a build-up kernel kb. The convolution is done with the energy

density distribution in terms of effective distance in the following way:

Eb(~p) =

∫ pz

t=0Etot(px, py, t)kb(deff)ρw(px, py, t)dt, (3.10)

where deff is the (signed) effective distance from (px, py, pz) to (px, py, t),

and the multiplication with ρw is due to the change of variables from effec-

tive depth to true depth. This correction effectively shifts energy deeper,

so the original pencil beams would no longer be accurately reproduced.

For example, the original build-up at the surface of the pencil beam would

be further stretched. Hence, it is necessary to pre-compensate in the I

function in (3.2) using a deconvolution approach.

3.4 Computational considerations

3.4.1 Performance characteristics

In this section, computational complexity of various SC algorithms is re-

viewed. For the purpose of the analysis, a 3D calculation grid N ×N ×Nwill be considered with M number of rays for ray-tracing for scatter scal-

ing and G is the number of energy groups. The Table 3.1 contains the

computational complexities of the various dose calculation algorithms.

An example of running time of a computer implementation of the PB

method in VI is about 10 s for a 40 × 40 mm2 field and about 60 s for a

31

Model-based convolution and superposition methods in absorbed dose calculation

Table 3.1. Computational complexity of different dose deposition algorithms

Algorithm Complexity

Discrete convolution N6

Discrete FFT convolution kN3 logN3

Ray-traced scaled 3D SC N7

CCC MN4

AAATM MN3

AcurosXBTM (Deterministic Transport Solver) GMN3

400× 400 mm2 field, respectively (on a dual-core Intel Xeon 5160 platform

with 8 GB of memory and two processors).

3.4.2 Parallel computing

The performance of computers has increased dramatically during the life-

time of semiconductor based computing. The improvements were mainly

driven by improving clock speed and larger and faster memory access. The

increase in speed using these methods is, however, at its limit due to en-

ergy consumption and heat emission of processing chips as well as other

physical limitations. In recent years, parallel computing has emerged as

an alternative approach to further boost performance.

Central processing unit (of a computer) (CPU) of computers currently

have multiple processor cores to allow for parallelism. Another mani-

festation of the parallel computing architecture is a Graphics processing

unit (GPU). The GPU has evolved from its origin in computer graphics

and visualization to a general purpose parallel computing device. Compu-

tationally challenging scientific problems have been widely solved using

GPU technology in recent years. It has also been successfully employed in

the radiotherapy domain. The various radiotherapy applications of GPU

technology have been reviewed by Pratx and Xing (2011) and Jia et al.

(2014).

The radiation dose calculation methods can be formulated in such a

way that data parallel implementations on GPU platforms are possible.

This has been an active area of research in the past few years. Jia et

al. (2011) have implemented MC calculation method in GPU and report

almost two orders of magnitude speed up compared to CPU based compu-

tation. Hissoiny et al. (2009), Hissoiny et al. (2010), Jacques et al. (2011),

and Chen et al. (2012) report of GPU implementations of the SC method.

32

Model-based convolution and superposition methods in absorbed dose calculation

Additionally, Chen et al. (2011) report an extremely efficient implementa-

tion of the CCC algorithm, where calculation times can be pushed below 1

s per beam for a grid of 2563 calculation points on modern GPU platforms

(NVIDIA GTX295). Gu et al. (2009) has applied GPU technology to suc-

cessfully implement an ultra-fast dose calculation engine using the PB

method. These developments open up new opportunities for interactive

dose shaping tools and more accurate solutions to the inverse problems in

radiotherapy treatment planning.

33

Model-based convolution and superposition methods in absorbed dose calculation

34

4. Summary of results

4.1 Patient-specific distributions in radionuclide therapy

The first aim for this research was to produce a dose planning system for

radioimmunotherapy by leveraging an existing radiotherapy treatment

planning system and implementing a faster dose kernel convolution algo-

rithm. The aim was also to develop novel 3D absorbed dose visualization

methods. The results reported in I were a successful implementation of

a radionuclide therapy planning system utilizing a fast point dose ker-

nel calculation method and expanding visualization and user interface of

the existing radiotherapy TPS. The developed system was used to ana-

lyze variability of biological uptake and clearance of the therapy agent

in various patients and to estimate absorbed doses based on a point dose

kernel dose calculation method in II. The main results were that both the

inter-patient variability of biological clearance and localized differences

for individual patients warrant the use of serial SPECT imaging to be

able to determine patient-specific absorbed doses.

The clearance times for two different patients are plotted in Figure 1

of II. The clearance is assumed to contain two exponential components,

thus the biological half-lives was calculated for both components. The ex-

ponential trend for the clearance determined from the SPECT images is

also shown in the same figure. Spatial variation of the activity clearance

was analyzed in the intra-therapeutic SPECT images by dividing the im-

ages into sub-volumes 64 cm3 (4 x 4 x 4 cm). The biological half-lives

and clearance times of for each of these sub-volumes were calculated and

the results are summarized in Table 1 (II). Additionally, patient absorbed

doses were calculated based on cumulated activity and the activity map

from the first SPECT study.

35

Summary of results

Figure 4.1. A dose distribution for Y-90 radionuclide therapy visualized superimposedwith CT image and a 3D rendering of the dose cloud with patient anatomy.Reprinted with permission from IV

.

Further analysis was preformed to compare the patient-specific dose

calculation dose kernel method with a widely used MIRD S-factor model

method for patients receiving monoclonal antibody therapy in III. The re-

sults indicate that on the average the model-based methods agree with the

patient-specific method, but looking at an individual patient level there

are large variations between the methods.The variation of the macro-

scopic absorbed dose analysis yielded an average of the minimum doses

to be 50% and the average of maximums to be 175% of the average dose

in the organ. In some patients, the variation was especially larger in

the larger organs such as the liver and spleen. The maximum variation

within these organs was found to be 20% – 436%.

The same methods were then applied to a different type of radionuclide

therapy of recurrent hepatoblastoma with Y-90 in IV, with results indicat-

ing similar patient to patient variations as seen in II and III, pointing to

the short-comings of the model-based MIRD S-factor methodology. The

calculated MIRD Y-90 doses were for cardiac wall 0.75 Gy, liver 0.62 Gy,

spleen 0.51Gy, and bone marrow 0.053 Gy, with the effective whole body

dose at 0.18 Gy, i.e. 4.23 mGy/MBq. The patient-specific method demon-

strated the mean doses in normal tissues as follows: heart 0.58 Gy, liver

0.48 Gy, spleen 0.37 Gy, and bone marrow 0.34 Gy. Dose volume his-

tograms for the different organs were calculated, for instance the actual

36

Summary of results

liver tumor dose was in average 0.51 Gy, with a range 0.22-0.96 Gy. A

visualization of the calculated doses is shown in Figure 4.1.

4.2 A pencil beam superposition algorithm in external radiotherapy

The development of a PB dose calculation method for external photon

therapy was undertaken in V and further refined in VI. The earlier paper

outlines the methods and foundations of the density-scaling methodology

of the pencil beams and depth-dependent component.

As presented in VI, there is generally a good agreement between the

calculations utilizing the presented method and MC simulations in differ-

ent kind of heterogeneous phantoms. Most of the observed discrepancies

were within (2%, 2 mm), where the dose difference is specified with re-

spect to the field Central axis (CAX) dmax. Considerably larger deviations

were found only in the central axis depth dose of the smallest field size

(30×30 mm2) in the lung slab phantom for the 18 MV beam, where discrep-

ancies in the order of 8% were observed inside the lung insert (ρw = 0.3).

These discrepancies are of comparable magnitude (∼5%), as observed by

Arnfield et al. (2000), for the CCC superposition model in similar situa-

tions. The explanation for the discrepancies lies in the fact that in high

energy beams of small field size there is a loss of electronic equilibrium

on the central axis, which is not modeled with rectilinear kernel scaling

approaches. The electronic disequilibrium on the field central axis in the

low-density material becomes larger as the field size decreases and the

beam energy increases and there are more electrons traveling away from

the corresponding volume element on the central axis than towards it.

The re-buildup effect is overestimated in our method on the lung-water

interface, as seen in Figure 4.2, which is contrary to other SC models that

tend to underestimate the effect. This difference in the algorithm behav-

ior is due to the build-up kernel correction method used in the presented

method, which is not used in other SC algorithms. The build-up kernel

has been designed such that the build-up between vacuum and water is

correctly reproduced, whereas the build-up effect between lung and water

is probably smaller, which could explain the observed overestimation in

the re-buildup region. Fotina et al. (2009) provided comparisons between

AAA and SC methods to MC calculations, that show good agreement for

both of the methods with slightly better agreement for the SC method.

In higher density material (bone, ρw = 1.85) the discrepancies between

37

Summary of results

20

40

60

80

100

0 50 100 150 200 250 300-8

-6

-4

-2

0

2

4

6

8

Per

cent

dep

th d

ose

(%)

Diff

eren

ce (%

)

Depth (mm)

(a)

AAA Fs30VMC Fs30

Diff Fs30

20

40

60

80

100

0 50 100 150 200 250 300-8

-6

-4

-2

0

2

4

6

8

Per

cent

dep

th d

ose

(%)

Diff

eren

ce (%

)

Depth (mm)

(b)

AAA Fs50VMC Fs50

Diff Fs50

20

40

60

80

100

0 50 100 150 200 250 300-8

-6

-4

-2

0

2

4

6

8

Per

cent

dep

th d

ose

(%)

Diff

eren

ce (%

)

Depth (mm)

(c)

AAA Fs100VMC Fs100

Diff Fs100

20

40

60

80

100

0 50 100 150 200 250 300-8

-6

-4

-2

0

2

4

6

8

Per

cent

dep

th d

ose

(%)

Diff

eren

ce (%

)

Depth (mm)

(d)

AAA Fs200VMC Fs200

Diff Fs200

Figure 4.2. Calculated ’AAA’ and MC-simulated ’VMC’ depth dose curves in the lung slabphantom for the 6 MV beam. (a) Field size 30× 30 mm2, (b) 50× 50 mm2, (c)100× 100 mm2, and (d) 200× 200 mm2. Reprinted with permission from VI.

our PB algorithm and MC simulations are in the order of (2%, 2 mm).

For lower energies (6 MV beam), our method overestimates the dose sys-

tematically about 1% inside the high-density material. For higher energy

(18 MV), the discrepancies near the heterogeneity border of the bone slab

phantom are smaller.

When compared to previously published experimental verification of

the presented method, some agreements and some disagreements were

found. In the work of Van Esch et al. (2006), the current method was

compared to ionization chamber and film measurements in several homo-

geneous and heterogeneous phantoms. The lateral profile comparisons

in the phantom with cork insert are in good agreement with the results

in the lung block phantom shown in Figure 4.3. The corresponding depth

dose comparisons for 6 MV show a significantly better agreement with the

MC simulations in the work than the comparisons to ionization chamber

measurements presented by Van Esch et al. (2006). This apparent contra-

diction can be explained by the fact that the ionization chamber itself can

cause significant dose perturbations (6 . . . 12%) at the point of measure-

ment in case of electronic disequilibrium. These kinds of perturbations

occur especially for a small field size, in low-density media.

The main results for the methods in V and VI are that excellent agree-

38

Summary of results

0

10

20

30

40

50

60

70

80

90

-200 -150 -100 -50 0 50 100 150 200-8

-6

-4

-2

0

2

4

6

8

Rel

ativ

e do

se (%

)

Diff

eren

ce (%

)

Depth (mm)

(a)

AAA D100VMC D100

Diff D100

0

10

20

30

40

50

60

70

80

-200 -150 -100 -50 0 50 100 150 200-8

-6

-4

-2

0

2

4

6

8

Rel

ativ

e do

se (%

)

Diff

eren

ce (%

)

Depth (mm)

(b)

AAA D160VMC D160

Diff D160

0

20

40

60

80

100

-200 -150 -100 -50 0 50 100 150 200-8

-6

-4

-2

0

2

4

6

8

Rel

ativ

e do

se (%

)

Diff

eren

ce (%

)

Depth (mm)

(c)

AAA D75VMC D75

Diff D75

0

10

20

30

40

50

60

70

80

90

-200 -150 -100 -50 0 50 100 150 200-8

-6

-4

-2

0

2

4

6

8

Rel

ativ

e do

se (%

)

Diff

eren

ce (%

)

Depth (mm)

(d)

AAA D110VMC D110

Diff D110

Figure 4.3. Calculated ’AAA’ and MC-simulated ’VMC’ dose profiles in the lung blockphantom for 6 and 18 MV beams. (a) 6 MV, depth 100 mm (b) 6 MV, depth160 mm, (c) 18 MV, depth 100 mm, and (d) 18 MV, depth 160 mm. Reprintedwith permission from VI

ment with MC method and experiments are obtained in homogenous ma-

terial as well as good results for the lateral heterogeneities (both water-

lung and water-bone interfaces) are obtained with lateral scaling of scat-

ter kernels. The method is computationally very efficient for use in a

routine clinical setting.

39

Summary of results

40

5. Discussion and conclusions

5.1 Overall results

The aims of the Thesis were to develop methods to improve dose calcu-

lation in aiding treatment planning of radionuclide and external-beam

therapy. The aims of the Thesis were met and a high level summary of

results in relation to the aims is presented in Figure 5.1.

The Thesis developed methodology for 3D treatment planning of ra-

dionuclide therapy with dose calculation based on quantitative SPECT

images and a point dose kernel calculation method. The dose kernel con-

volution method was applied in several radionuclide therapy cases as a

treatment planning and dosimetric verification tool. Comparisons of the

developed patient-specific dose calculation method with the widely used

MIRD S-factor model was discussed in III and IV. The results show large

variations between the methods at individual patient level and within

target organs. The results indicate that the spatial dose distribution is

needed to further understand therapeutic effect and toxicity of radionu-

clide treatments, and the developed system is useful in the analysis of

radionuclide treatments.

The development of a PB dose kernel based calculation method for ex-

ternal photon therapy that also accounts for local variations in tissue ma-

terial densities in 3D space was reported in V and further refined in VI.

The method performs within clinically acceptable accuracy as compared

to experiments and MC calculations with typical agreement within (2%,

2 mm) for various test problems.

Although the aims of the Thesis were met, there is further room for im-

provement in the source modeling of the radionuclide therapy (i.e. quan-

titative SPECT and automated processing of time-series activity data).

41

Discussion and conclusions

The recent advances in nuclear medicine imaging with hybrid SPECT/CT

devices and PET imaging are enabling this advancement. For instance

Willowson et al. (2008) report on an experimental verification of quantita-

tive methodology based on SPECT/CT that achieves accuracy of activity

quantification in the range of -7%–%4, compared to known activity con-

centrations.

• Implemention of point dose kernel based radionuclide TPS

• Powerful toolset for evaluaton of patient specific 3D dose distiributions

AAim 1. Radionuclide 3D planning methods

• Different therapy cases using point kernel and S-factor methods

• Point kernel methods provide patient specific 3D information for various radionuclides

Aim 2. Radionuclide

therapy case studies

• PB method with 3D heterogeneity correction

• Comparisons to MC calculations show good agreement

• Fast calculation times & wide clinical adoption

Aim 3. External beam dose

computations

Figure 5.1. Main results grouped by the aims of the Thesis.

5.2 Contribution to the field

This Thesis has developed further computational methods that are rele-

vant in the practical application of radionuclide therapy as well external-

beam therapy. Applying the methods in radionuclide therapy has pro-

vided new results on the applicability of the methods as well as a compar-

ison to existing practices of the MIRD formalism.

The application of patient-specific dosimetry in radionuclide therapy

is still in its infancy in the wider clinical practice of 2016. Although the

methods developed as part of this Thesis have been used in clinical prac-

tice since 1997, wider adoption will only be possible when these meth-

ods are introduced in an easy to use commercial package (by Nuclear

Medicine image analysis or general radiotherapy planning software ven-

42

Discussion and conclusions

dors). The work in papers I — IV show that this approach is viable and

is well aligned with toolsets available in radiotherapy planning software

systems.

In papers V and VI a computationally efficient and accurate PB al-

gorithm was developed with 3D treatment of tissue heterogeneity. It is

coupled with an accurate model of the external radiation therapy ma-

chine sources including a robust optimization of the model parameters

described in Tillikainen et al. (2007). It has been commercialized as the

AAA dose calculation algorithm in the widely used EclipseTM Treatment

planning system (Varian Medical Systems, Palo Alto CA). The methods

are used in routine clinical practice — with thousands of treatment plans

calculated daily using these methods and numerous of studies examining

its performance (Ojala et al. 2014; Tsuruta et al. 2014; Liu et al. 2014;

Han et al. 2012; Fotina et al. 2009; Breitman et al. 2007; Van Esch et al.

2006, etc.). Its main contribution is the novel treatment of heterogeneity

with a good balance between speed and accuracy.

5.3 Future directions

Although more rigorous and complete solutions to the radiation transport

exists (see Section 1.6), the model-based superposition and convolution

methods continue have an important role in the radiotherapy modeling.

In the past two decades, they have been the workhorses for dose calcula-

tion as well basis for solutions of the inverse problems. In the future, their

computational efficiency will ensure that they have a role in interactive

use as well as in radiotherapy plan optimization solutions. The methods

also lend themselves for efficient parallel computing implementations, as

discussed in Section 3.4.2.

External-beam radiotherapy has transitioned into image guided ther-

apy and the increased information of the daily patient setup will lend

itself for adaptation of the treatment plan for the current patient state.

This requires advances in rapid and automated dose evaluation, including

quick dose calculation and possible treatment plan optimization. These

computations need to happen in a few seconds in order not to delay the

daily patient treatment. The SC and PB methods are well poised for these

scenarios. These needs are also aligned with the adoption of ultra-high

dose fractions of the Stereotactic body radiation therapy (SBRT) (Lo et al.

2010).

43

Discussion and conclusions

Further improvements in accuracy could potentially be realized by com-

bining transport equation solvers with extremely fast convolution meth-

ods. The approach would perhaps improve the accuracy and modeling of

the relevant physics without compromising the speed of the methods to

provide fine details of the high resolution shape of the primary photon

energy fluence.

Next steps in improving the understanding and radiation dose thera-

peutic efficacy in radionuclide therapy is to adopt more widely the meth-

ods outlined in this Thesis. After that initial step, the next area to im-

prove is the process of acquiring quantitative 3D activity distributions

and their use in the patient-specific dose evaluation. Although the accu-

racy of the dose calculation is currently not the limiting factor, the mod-

eling of the radiation transport could be further enhanced by employing

direct solutions to the transport equation by MC methods or deterministic

solutions.

5.4 Conclusions

The methods developed in this Thesis have proven to be relevant in the

application of radiotherapy. Their relevance for the upcoming improve-

ments in overall radiotherapy applications is also foreseen due to their

computational efficiency. Other methods will complement these as the

computational power available increases over the upcoming years. Accu-

racy and efficacy of radiotherapy can be enhanced when physical modeling

is further improved and applied in clinical practice.

44

References

Ahnesjö, A. (1989). “Collapsed cone convolution of radiant energy for pho-

ton dose calculation in heterogeneous media.” Med Phys 16.4, pp. 577–

592.

Ahnesjö, A. and M. M. Aspradakis (1999). “Dose calculations for external

photon beams in radiotherapy.” Phys Med Biol 44.11, R99–155.

Ahnesjö, A., P. Andreo, and A. Brahme (1987). “Calculation and applica-

tion of point spread functions for treatment planning with high energy

photon beams.” Acta Oncol 26.1, pp. 49–56.

Ahnesjö, A., M. Saxner, and A. Trepp (1992). “A pencil beam model for

photon dose calculation.” Med Phys 19.2, pp. 263–273.

Ahnesjö, A., L. Weber, A. Murman, M. Saxner, I. Thorslund, and E. Tra-

neus (2005). “Beam modeling and verification of a photon beam multi-

source model.” Med Phys 32.6, pp. 1722–1737.

Andreo, P. (1991). “Monte Carlo techniques in medical radiation physics.”

Phys Med Biol 36.7, pp. 861–920.

Arnfield, M. R., C. H. Siantar, J. Siebers, P. Garmon, L. Cox, and R. Mohan

(2000). “The impact of electron transport on the accuracy of computed

dose.” Med Phys 27.6, pp. 1266–1274.

Atun, R., D. A. Jaffray, M. B. Barton, F. Bray, M. Baumann, B. Vikram,

T. P. Hanna, F. M. Knaul, Y. Lievens, T. Y. M. Lui, M. Milosevic, B.

O’Sullivan, D. L. Rodin, E. Rosenblatt, J. Van Dyk, M. L. Yap, E. Zu-

bizarreta, and M. Gospodarowicz (2015). “Expanding global access to

radiotherapy.” Lancet Oncol 16.10, pp. 1153–1186.

Beekman, F. J., H. W. A. M. de Jong, and S. van Geloven (2002). “Effi-

cient fully 3-D iterative SPECT reconstruction with Monte Carlo-based

scatter compensation”. Medical Imaging, IEEE Transactions on 21.8,

pp. 867–877.

45

REFERENCES

Boyer, A. L. (1984). “Shortening the calculation time of photon dose dis-

tributions in an inhomogeneous medium.” Med Phys 11.4, pp. 552–554.

Boyer, A. L. and E. C. Mok (1985). “A photon dose distribution model em-

ploying convolution calculations.” Med Phys 12.2, pp. 169–177.

Boyer, A. L. and E. C. Mok (1986a). “Brachytherapy seed dose distribu-

tion calculation employing the fast Fourier transform”. Med Phys 13,

pp. 525–529.

Boyer, A. L. and E. C. Mok (1986b). “Calculation of photon dose distribu-

tions in an inhomogeneous medium using convolutions.” Med Phys 13.4,

pp. 503–509.

Boyer, A. L., Y. P. Zhu, L. Wang, and P. Francois (1989). “Fast Fourier

transform convolution calculations of x-ray isodose distributions in ho-

mogeneous media.” Med Phys 16.2, pp. 248–253.

Breitman, K., S. Rathee, C. Newcomb, B. Murray, D. Robinson, C. Field,

H. Warkentin, S. Connors, M. Mackenzie, P. Dunscombe, and G. Fallone

(2007). “Experimental validation of the Eclipse AAA algorithm.” J Appl

Clin Med Phys 8.2, pp. 76–92.

Cade, S. C., S. Arridge, M. J. Evans, and B. F. Hutton (2013). “Use of

measured scatter data for the attenuation correction of single photon

emission tomography without transmission scanning.” Med Phys 40.8,

p. 082506.

Carlsson, A. K. and A. Ahnesjö (2000a). “Point kernels and superposition

methods for scatter dose calculations in brachytherapy.” Phys Med Biol

45.2, pp. 357–382.

Carlsson, A. K. and A. Ahnesjö (2000b). “The collapsed cone superposition

algorithm applied to scatter dose calculations in brachytherapy.” Med

Phys 27.10, pp. 2320–2332.

Chen, Q., M. Chen, and W. Lu (2011). “Ultrafast convolution/ superposi-

tion using tabulated and exponential kernels on GPU.” Med Phys 38.3,

pp. 1150–1161.

Chen, Q., W. Lu, Y. Chen, M. Chen, D. Henderson, and E. Sterpin (2012).

“Validation of GPU based TomoTherapy dose calculation engine.” Med

Phys 39.4, pp. 1877–1886.

Cheng, L., R. F. Hobbs, G. Sgouros, and E. C. Frey (2014). “Development

and evaluation of convergent and accelerated penalized SPECT image

reconstruction methods for improved dose-volume histogram estimation

in radiopharmaceutical therapy.” Med Phys 41.11, p. 112507.

46

REFERENCES

Chiavassa, S., M. Bardi, F. Guiraud-Vitaux, D. Bruel, J.-R. Jourdain, D.

Franck, and I. Aubineau-Lani (2005). “OEDIPE: a personalized dosimet-

ric tool associating voxel-based models with MCNPX.” Cancer Biother

Radiopharm 20.3, pp. 325–332.

Deng, J., T. Guerrero, C. M. Ma, and R. Nath (2004). “Modelling 6 MV pho-

ton beams of a stereotactic radiosurgery system for Monte Carlo treat-

ment planning.” Phys Med Biol 49.9, pp. 1689–1704.

Dewaraja, Y. K., E. C. Frey, G. Sgouros, A. B. Brill, P. Roberson, P. B.

Zanzonico, and M. Ljungberg (2012). “MIRD Pamphlet No. 23: Quanti-

tative SPECT for Patient-Specific 3-Dimensional Dosimetry in Internal

Radionuclide Therapy.” J Nucl Med 53.8, pp. 1310–1325.

Dieudonné, A., R. F. Hobbs, R. Lebtahi, F. Maurel, S. Baechler, R. L. Wahl,

A. Boubaker, D. Le Guludec, G. Sgouros, and I. Gardin (2013). “Study of

the impact of tissue density heterogeneities on 3-dimensional abdomi-

nal dosimetry: comparison between dose kernel convolution and direct

Monte Carlo methods.” J Nucl Med 54.2, pp. 236–243.

Drzymala, R. E., R. Mohan, L. Brewster, J. Chu, M. Goitein, W. Harms,

and M. Urie (1991). “Dose-volume histograms.” Int J Radiat Oncol Biol

Phys 21.1, pp. 71–78.

Erdi, A. K., E. D. Yorke, M. H. Loew, Y. E. Erdi, M. Sarfaraz, and B. W.

Wessels (1998). “Use of the fast Hartley transform for three-dimensional

dose calculation in radionuclide therapy”. Med Phys 25.11, pp. 2226–

2233.

Erdi, E. K., M. Loew, E. Yorke, Y. Erdi, and B. Wessels (1994). “Use of

the fast Hartley transform for efficient 3D convolution in calculation

of radiation dose”. Proc. 16th Annual IEEE-EMBS Conference. IEEE.

Piscataway, NJ: IEEE, pp. 639–640.

Erlandsson, K., I. Buvat, P. H. Pretorius, B. A. Thomas, and B. F. Hutton

(2012). “A review of partial volume correction techniques for emission

tomography and their applications in neurology, cardiology and oncol-

ogy.” Phys Med Biol 57.21, R119–R159.

Fippel, M., I. Kawrakow, and K. Friedrich (1997). “Electron beam dose

calculations with the VMC algorithm and the verification data of the

NCI working group.” Phys Med Biol 42.3, pp. 501–520.

Fippel, M., W. Laub, B. Huber, and F. Nüsslin (1999). “Experimental inves-

tigation of a fast Monte Carlo photon beam dose calculation algorithm.”

Phys Med Biol 44.12, pp. 3039–3054.

47

REFERENCES

Fippel, M., F. Haryanto, O. Dohm, F. Nuesslin, and S. Kriesen (2003). “A

virtual photon energy fluence model for Monte Carlo dose calculation.”

Med Phys 30.3, pp. 301–311.

Fix, M. K., M. Stampanoni, P. Manser, E. J. Born, R. Mini, and P. Rüegseg-

ger (2001a). “A multiple source model for 6 MV photon beam dose calcu-

lations using Monte Carlo.” Phys Med Biol 46.5, pp. 1407–1427.

Fix, M. K., P. Manser, E. J. Born, R. Mini, and P. Rüegsegger (2001b).

“Monte Carlo simulation of a dynamic MLC based on a multiple source

model.” Phys Med Biol 46.12, pp. 3241–3257.

Fix, M. K., P. J. Keall, K. Dawson, and J. V. Siebers (2004). “Monte Carlo

source model for photon beam radiotherapy: photon source characteris-

tics.” Med Phys 31.11, pp. 3106–3121.

Fix, M. K., D. Frei, W. Volken, H. Neuenschwander, E. Born, and P. Manser

(2010). “Monte Carlo dose calculation improvements for low energy elec-

tron beams using eMC.” Phys Med Biol 55.16, pp. 4577–4588.

Fotina, I., P. Winkler, T. Künzler, J. Reiterer, I. Simmat, and D. Georg

(2009). “Advanced kernel methods vs. Monte Carlo-based dose calcula-

tion for high energy photon beams.” Radiother Oncol 93.3, pp. 645–653.

Furhang, E. E., C. S. Chui, and G. Sgouros (1996a). “A Monte Carlo ap-

proach to patient-specific dosimetry”. Med Phys 23, pp. 1523–1529.

Furhang, E. E., G. Sgouros, and C. S. Chui (1996b). “Radionuclide photon

dose kernels for internal emitter dosimetry”. Med Phys 23, pp. 759–764.

Furhang, E. E., C. S. Chui, K. S. Kolbert, S. M. Larson, and G. Sgouros

(1997). “Implementation of a Monte Carlo dosimetry method for patient-

specific internal emitter therapy”. Med Phys 24.7, pp. 1163–1172.

Gardin, I., L. G. Bouchet, K. Assié, J. Caron, A. Lisbona, L. Ferrer, W.

E. Bolch, and P. Vera (2003). “Voxeldoes: a computer program for 3-D

dose calculation in therapeutic nuclear medicine.” Cancer Biother Ra-

diopharm 18.1, pp. 109–115.

Georg, D., T. Nyholm, J. Olofsson, F. Kjaer-Kristoffersen, B. Schneken-

burger, P. Winkler, H. Nyström, A. Ahnesjö, and M. Karlsson (2007).

“Clinical evaluation of monitor unit software and the application of ac-

tion levels.” Radiother Oncol 85.2, pp. 306–315.

Giap, H. B., D. J. Macey, and D. A. Podoloff (1995a). “Development of

a SPECT-based three-dimensional treatment planning system for ra-

dioimmunotherapy”. J Nucl Med 36, pp. 1885–1894.

48

REFERENCES

Giap, H. B., D. J. Macey, J. E. Bayouth, and A. L. Boyer (1995b). “Valida-

tion of a dose-point kernel convolution technique for internal dosimetry”.

Phys Med Biol 40, pp. 365–381.

Grimes, J. and A. Celler (2014). “Comparison of internal dose estimates

obtained using organ-level, voxel S value, and Monte Carlo techniques.”

Med Phys 41.9, p. 092501.

Gu, X., D. Choi, C. Men, H. Pan, A. Majumdar, and S. B. Jiang (2009).

“GPU-based ultra-fast dose calculation using a finite size pencil beam

model.” Phys Med Biol 54.20, pp. 6287–6297.

Guy, M. J., G. D. Flux, P. Papavasileiou, M. A. Flower, and R. J. Ott (2003).

“RMDP: a dedicated package for 131I SPECT quantification, registra-

tion and patient-specific dosimetry.” Cancer Biother Radiopharm 18.1,

pp. 61–69.

Halperin, E. C., C. A. Perez, and L. W. Brady (2008). Perez and Brady’s

Principles and Practice of Radiation Oncology. Philadelphia, PA: Lip-

pincott Williams & Wilkins.

Han, T., F. Mourtada, K. Kisling, J. Mikell, D. Followill, and R. Howell

(2012). “Experimental validation of deterministic Acuros XB algorithm

for IMRT and VMAT dose calculations with the Radiological Physics

Center’s head and neck phantom.” Med Phys 39.4, pp. 2193–2202.

Hissoiny, S., B. Ozell, and P. Després (2009). “Fast convolution-superposition

dose calculation on graphics hardware.” Med Phys 36.6, pp. 1998–2005.

Hissoiny, S., B. Ozell, and P. Després (2010). “A convolution-superposition

dose calculation engine for GPUs.” Med Phys 37.3, pp. 1029–1037.

Hubbell, J. H. and S. M. Seltzer (1996). Tables of X-ray Mass Attenuation

Coefficients and Mass Energy-Absorption Coefficients from 1 keV to 20

MeV for Elements Z = 1 to 92 and 48 Additional Substances of Dosimetric

Interest. URL: http://physics.nist.gov/PhysRefData/XrayMassCoef/

cover.html.

Humm, J. L., J. C. Roeske, D. R. Fisher, and G. T. Chen (1993). “Microdosi-

metric concepts in radioimmunotherapy”. Med Phys 20.2 Pt 2, pp. 535–

541.

Hutton, B. F., I. Buvat, and F. J. Beekman (2011). “Review and current

status of SPECT scatter correction.” Phys Med Biol 56.14, R85–112.

ICRU (1988). Fundamental quantities and units for ionizing radiation

ICRU Publication 60. Bethesda, MD: International Commission on Ra-

diation Units and Measurements.

49

REFERENCES

Jackson, P. A., J.-M. Beauregard, M. S. Hofman, T. Kron, A. Hogg, and R.

J. Hicks (2013). “An automated voxelized dosimetry tool for radionuclide

therapy based on serial quantitative SPECT/CT imaging.” Med Phys

40.11, p. 112503.

Jacques, R., J. Wong, R. Taylor, and T. McNutt (2011). “Real-time dose

computation: GPU-accelerated source modeling and superposition/ con-

volution.” Med Phys 38.1, pp. 294–305.

Jia, X., X. Gu, Y. J. Graves, M. Folkerts, and S. B. Jiang (2011). “GPU-

based fast Monte Carlo simulation for radiotherapy dose calculation.”

Phys Med Biol 56.22, pp. 7017–7031.

Jia, X., P. Ziegenhein, and S. B. Jiang (2014). “GPU-based high-performance

computing for radiation therapy.” Phys Med Biol 59.4, R151–R182.

Jiang, S. B., A. L. Boyer, and C. M. Ma (2001). “Modeling the extrafocal

radiation and monitor chamber backscatter for photon beam dose calcu-

lation.” Med Phys 28.1, pp. 55–66.

Kawrakow, I. and M. Fippel (2000). “VMC++, a fast MC algorithm for Ra-

diation Treatment planning”. The Use of Computers in Radiation Ther-

apy. Ed. by W. Schlegel and T. Bortfeld. Springer Berlin Heidelberg,

pp. 126–128.

Kletting, P., S. Schimmel, H. A. Kestler, H. Hänscheid, M. Luster, M.

Fernez, J. H. Bröer, D. Nosske, M. Lassmann, and G. Glatting (2013).

“Molecular radiotherapy: the NUKFIT software for calculating the time-

integrated activity coefficient.” Med Phys 40.10, p. 102504.

Kolbert, K. S., G Sgouros, A. M. Scott, J. E. Bronstein, R. A. Malane, J

Zhang, H Kalaigian, S McNamara, L Schwartz, and S. M. Larson (1997).

“Implementation and evaluation of patient-specific three-dimensional

internal dosimetry”. J Nucl Med 38.2, pp. 301–308.

Kotiluoto, P., J. Pyyry, and H. Helminen (2007). “MultiTrans SP3 code

in coupled photon-electron transport problems”. Radiation Physics and

Chemistry 76, pp. 9–14.

Leichner, P. K., K. F. Koral, R. J. Jaszczak, A. J. Green, G. T. Chen, and

J. C. Roeske (1993). “An overview of imaging techniques and physical

aspects of treatment planning in radioimmunotherapy”. Med Phys 20.2

Pt 2, pp. 569–577.

Leichner, P. (1994). “A unified approach to photon and beta particle dosime-

try”. J Nucl Med 35, pp. 1721–1729.

Lemaréchal, Y., J. Bert, C. Falconnet, P. Després, A. Valeri, U. Schick, O.

Pradier, M.-P. Garcia, N. Boussion, and D. Visvikis (2015). “GGEMS-

50

REFERENCES

Brachy: GPU GEant4-based Monte Carlo simulation for brachytherapy

applications.” Phys Med Biol 60.13, pp. 4987–5006.

Liu, H. H., T. R. Mackie, and E. C. McCullough (1997). “A dual source

photon beam model used in convolution/superposition dose calculations

for clinical megavoltage x-ray beams.” Med Phys 24.12, pp. 1960–1974.

Liu, H. H., T. R. Mackie, and E. C. McCullough (2000). “Modeling pho-

ton output caused by backscattered radiation into the monitor chamber

from collimator jaws using a Monte Carlo technique.” Med Phys 27.4,

pp. 737–744.

Liu, H.-W., Z. Nugent, R. Clayton, P. Dunscombe, H. Lau, and R. Khan

(2014). “Clinical impact of using the deterministic patient dose calcula-

tion algorithm Acuros XB for lung stereotactic body radiation therapy.”

Acta Oncol 53.3, pp. 324–329.

Ljungberg, M., M. King, G. Hademenos, and S. Strand (1994). “Compari-

son of four scatter correction methods using monte carlo simulated source

distributions”. J Nucl Med 35, pp. 143–151.

Ljungberg, M., K. Sjögreen, X. Liu, E. Frey, Y. Dewaraja, and S.-E. Strand

(2002). “A 3-dimensional absorbed dose calculation method based on

quantitative SPECT for radionuclide therapy: evaluation for (131)I us-

ing monte carlo simulation.” J Nucl Med 43.8, pp. 1101–1109.

Lo, S. S., A. J. Fakiris, E. L. Chang, N. A. Mayr, J. Z. Wang, L. Papiez,

B. S. Teh, R. C. McGarry, H. R. Cardenes, and R. D. Timmerman (2010).

“Stereotactic body radiation therapy: a novel treatment modality.” Nat

Rev Clin Oncol 7.1, pp. 44–54.

Loudos, G., I. Tsougos, S. Boukis, N. Karakatsanis, P. Georgoulias, K.

Theodorou, K. Nikita, and C. Kappas (2009). “A radionuclide dosime-

try toolkit based on material-specific Monte Carlo dose kernels.” Nucl

Med Commun 30.7, pp. 504–512.

Lubberink, M., H. Lundqvist, J. E. Westlin, V. Tolmachev, H. Schneider,

A. Lövqvist, A. Sundin, and J. Carlsson (1999). “Positron emission to-

mography and radio-immunotargeting – aspects of quantification and

dosimetry.” Acta Oncol 38.3, pp. 343–349.

Lundqvist, H., M. Lubberink, V. Tolmachev, A. Lövqvist, A. Sundin, S. Be-

shara, A. Bruskin, J. Carlsson, and J. E. Westlin (1999). “Positron emis-

sion tomography and radioimmunotargeting–general aspects.” Acta On-

col 38.3, pp. 335–341.

51

REFERENCES

Ma, C. M., E. Mok, A. Kapur, T. Pawlicki, D. Findley, S. Brain, K. Forster,

and A. L. Boyer (1999). “Clinical implementation of a Monte Carlo treat-

ment planning system.” Med Phys 26.10, pp. 2133–2143.

Macey, D. J., E. J. Grant, J. E. Bayouth, H. B. Giap, S. J. Danna, R. Siris-

riro, and D. A. Podoloff (1995). “Improved conjugate view quantitation

of I-131 by subtraction of scatter and septal penetration events with a

triple energy window method.” Med Phys 22.10, pp. 1637–1643.

Mackie, T. R., J. W. Scrimger, and J. J. Battista (1985). “A convolution

method of calculating dose for 15-MV x rays.” Med Phys 12.2, pp. 188–

196.

Mackie, T. R., A. F. Bielajew, D. W. Rogers, and J. J. Battista (1988). “Gen-

eration of photon energy deposition kernels using the EGS Monte Carlo

code.” Phys Med Biol 33.1, pp. 1–20.

Marcatili, S., C. Pettinato, S. Daniels, G. Lewis, P. Edwards, S. Fanti, and

E. Spezi (2013). “Development and validation of RAYDOSE: a Geant4-

based application for molecular radiotherapy.” Phys Med Biol 58.8, pp. 2491–

2508.

Mohan, R. and C. S. Chui (1987). “Use of fast Fourier transforms in calcu-

lating dose distributions for irregularly shaped fields for three-dimensional

treatment planning.” Med Phys 14.1, pp. 70–77.

Mohan, R., C. Chui, and L. Lidofsky (1985). “Energy and angular distri-

butions of photons from medical linear accelerators.” Med Phys 12.5,

pp. 592–597.

Nath, R., L. L. Anderson, G. Luxton, K. A. Weaver, J. F. Williamson, and

A. S. Meigooni (1995). “Dosimetry of interstitial brachytherapy sources:

recommendations of the AAPM Radiation Therapy Committee Task Group

No. 43. American Association of Physicists in Medicine.” Med Phys 22.2,

pp. 209–234.

Neuenschwander, H., T. R. Mackie, and P. J. Reckwerdt (1995). “MMC–a

high-performance Monte Carlo code for electron beam treatment plan-

ning.” Phys Med Biol 40.4, pp. 543–574.

Ojala, J. (2014). “Monte Carlo Simulations in Quality Assurance of Dosime-

try and Clinical Dose Calculations in Radiotherapy”. PhD thesis. Tam-

pere University of Technology.

Ojala, J. J., M. K. Kapanen, S. J. Hyödynmaa, T. K. Wigren, and M. A.

Pitkänen (2014). “Performance of dose calculation algorithms from three

generations in lung SBRT: comparison with full Monte Carlo-based dose

distributions.” J Appl Clin Med Phys 15.2, p. 4662.

52

REFERENCES

Ott, R. J. (1996). “Imaging technologies for radionuclide dosimetry”. Phys

Med Biol 41.10, pp. 1885–1894.

Ouyang, J., G. El Fakhri, and S. C. Moore (2007). “Fast Monte Carlo based

joint iterative reconstruction for simultaneous 99mTc/ 123I SPECT imag-

ing.” Med Phys 34.8, pp. 3263–3272.

Petrokokkinos, L., K. Zourari, E. Pantelis, A. Moutsatsos, P. Karaiskos,

L. Sakelliou, I. Seimenis, E. Georgiou, and P. Papagiannis (2011). “Dosi-

metric accuracy of a deterministic radiation transport based 192Ir brachy-

therapy treatment planning system. Part II: Monte Carlo and experi-

mental verification of a multiple source dwell position plan employing a

shielded applicator.” Med Phys 38.4, pp. 1981–1992.

Poon, E., J. F. Williamson, T. Vuong, and F. Verhaegen (2008). “Patient-

specific Monte Carlo dose calculations for high-dose-rate endorectal brachy-

therapy with shielded intracavitary applicator.” Int J Radiat Oncol Biol

Phys 72.4, pp. 1259–1266.

Pouget, J.-P., C. Lozza, E. Deshayes, V. Boudousq, and I. Navarro-Teulon

(2015). “Introduction to radiobiology of targeted radionuclide therapy.”

Front Med (Lausanne) 2, p. 12.

Pratx, G. and L. Xing (2011). “GPU computing in medical physics: a re-

view.” Med Phys 38.5, pp. 2685–2697.

Prideaux, A. R., H. Song, R. F. Hobbs, B. He, E. C. Frey, P. W. Laden-

son, R. L. Wahl, and G. Sgouros (2007). “Three-dimensional radiobiologic

dosimetry: application of radiobiologic modeling to patient-specific 3-

dimensional imaging-based internal dosimetry.” J Nucl Med 48.6, pp. 1008–

1016.

Reiner, D., M. Blaickner, and F. Rattay (2009). “Discrete beta dose ker-

nel matrices for nuclides applied in targeted radionuclide therapy (TRT)

calculated with MCNP5”. Med Phys 36.11, pp. 4890–4896.

Rivard, M. J., B. M. Coursey, L. A. DeWerd, W. F. Hanson, M. S. Huq,

G. S. Ibbott, M. G. Mitch, R. Nath, and J. F. Williamson (2004). “Up-

date of AAPM Task Group No. 43 Report: A revised AAPM protocol for

brachytherapy dose calculations.” Med Phys 31.3, pp. 633–674.

Rogers, D. W., B. A. Faddegon, G. X. Ding, C. M. Ma, J. We, and T. R.

Mackie (1995). “BEAM: a Monte Carlo code to simulate radiotherapy

treatment units.” Med Phys 22.5, pp. 503–524.

Rogers, D. W. O. (2006). “Fifty years of Monte Carlo simulations for medi-

cal physics.” Phys Med Biol 51.13, R287–R301.

53

REFERENCES

Seco, J. and P. M. Evans (2006). “Assessing the effect of electron density

in photon dose calculations.” Med Phys 33.2, pp. 540–552.

Sgouros, G., G. Barest, J. Thekkumthala, C. Chui, R. Mohan, R. E. Bigler,

and P. B. Zanzonico (1990). “Treatment planning for internal radionu-

clide therapy: three-dimensional dosimetry for nonuniformly distributed

radionuclides.” J Nucl Med 31.11, pp. 1884–1891.

Sgouros, G., S. Chiu, K. S. Pentlow, L. J. Brewster, H. Kalaigian, B. Bald-

win, F. Daghighian, M. C. Graham, S. M. Larson, and R. Mohan (1993).

“Three-dimensional dosimetry for radioimmunotherapy treatment plan-

ning”. J Nucl Med 34.9, pp. 1595–1601.

Sheikh-Bagheri, D. and D. W. O. Rogers (2002a). “Monte Carlo calculation

of nine megavoltage photon beam spectra using the BEAM code.” Med

Phys 29.3, pp. 391–402.

Sheikh-Bagheri, D. and D. W. O. Rogers (2002b). “Sensitivity of megavolt-

age photon beam Monte Carlo simulations to electron beam and other

parameters.” Med Phys 29.3, pp. 379–390.

Stabin, M. G., R. B. Sparks, and E. Crowe (2005). “OLINDA/EXM: the

second-generation personal computer software for internal dose assess-

ment in nuclear medicine.” J Nucl Med 46.6, pp. 1023–1027.

Storchi, P. and E. Woudstra (1996). “Calculation of the absorbed dose dis-

tribution due to irregularly shaped photon beams using pencil beam ker-

nels derived form basic beam data.” Phys Med Biol 41.4, pp. 637–656.

Storchi, P. R., L. J. van Battum, and E. Woudstra (1999). “Calculation of

a pencil beam kernel from measured photon beam data.” Phys Med Biol

44.12, pp. 2917–2928.

Strand, S. E., P. Zanzonico, and T. K. Johnson (1993a). “Pharmacokinetic

modeling”. Med Phys 20.2 Pt 2, pp. 515–527.

Strand, S. E., B. A. Jönsson, M. Ljungberg, and J. Tennvall (1993b). “Ra-

dioimmunotherapy dosimetry–a review.” Acta Oncol 32.7-8, pp. 807–

817.

Tagesson, M., M. Ljungberg, and S. E. Strand (1996). “A Monte-Carlo pro-

gram converting activity distributions to absorbed dose distributions in

a radionuclide treatment planning system.” Acta Oncol 35.3, pp. 367–

372.

Tedgren, A. K. C. and A. Ahnesjö (2003). “Accounting for high Z shields in

brachytherapy using collapsed cone superposition for scatter dose calcu-

lation.” Med Phys 30.8, pp. 2206–2217.

54

REFERENCES

Tillikainen, L., S. Siljamäki, H. Helminen, J. Alakuijala, and J. Pyyry

(2007). “Determination of parameters for a multiple-source model of

megavoltage photon beams using optimization methods.” Phys Med Biol

52.5, pp. 1441–1467.

Tillikainen, L. (2009). “Methods for Dose Calculation and Beam Charac-

terization in External Photon Beam Radiotherapy”. PhD thesis. Aalto

University.

Traino, A. C., S. Marcatili, C. Avigo, M. Sollini, P. A. Erba, and G. Mariani

(2013). “Dosimetry for nonuniform activity distributions: a method for

the calculation of 3D absorbed-dose distribution without the use of voxel

S-values, point kernels, or Monte Carlo simulations.” Med Phys 40.4,

p. 042505.

Tsuruta, Y., M. Nakata, M. Nakamura, Y. Matsuo, K. Higashimura, H.

Monzen, T. Mizowaki, and M. Hiraoka (2014). “Dosimetric comparison

of Acuros XB, AAA, and XVMC in stereotactic body radiotherapy for

lung cancer.” Med Phys 41.8, p. 081715.

Tuszynski, J. (2010). Mass Attenuation Coefficient of Iron with contribu-

tions sources of attenuation. Data from XCOM database. URL: http://

commons.wikimedia.org/wiki/File:Ironattenuation.PNG..

Van Esch, A., L. Tillikainen, J. Pyykkonen, M. Tenhunen, H. Helminen,

S. Siljamäki, J. Alakuijala, M. Paiusco, M. Lori, and D. P. Huyskens

(2006). “Testing of the analytical anisotropic algorithm for photon dose

calculation.” Med Phys 33.11, pp. 4130–4148.

Vassiliev, O. N., T. A. Wareing, J. McGhee, G. Failla, M. R. Salehpour, and

F. Mourtada (2010). “Validation of a new grid-based Boltzmann equation

solver for dose calculation in radiotherapy with photon beams.” Phys

Med Biol 55.3, pp. 581–598.

Verhaegen, F., R. Symonds-Tayler, H. H. Liu, and A. E. Nahum (2000).

“Backscatter towards the monitor ion chamber in high-energy photon

and electron beams: charge integration versus Monte Carlo simulation.”

Phys Med Biol 45.11, pp. 3159–3170.

Watson, E. E., M. G. Stabin, and J. A. Siegel (1993). “MIRD formulation”.

Med Phys 20.2 Pt 2, pp. 511–514.

WHO (2015). Cancer, Fact sheet No. 297. World Health Organization. URL:

http://www.who.int/mediacentre/factsheets/fs297/en/.

Williams, L. E., G. L. DeNardo, and R. F. Meredith (2008). “Targeted ra-

dionuclide therapy.” Med Phys 35.7, pp. 3062–3068.

55

REFERENCES

Willowson, K., D. L. Bailey, and C. Baldock (2008). “Quantitative SPECT

reconstruction using CT-derived corrections.” Phys Med Biol 53.12, pp. 3099–

3112.

Wong, E., Y. Zhu, and J. Van Dyk (1996). “Theoretical developments on

fast Fourier transform convolution dose calculations in inhomogeneous

media.” Med Phys 23.9, pp. 1511–1521.

Zourari, K., E. Pantelis, A. Moutsatsos, L. Petrokokkinos, P. Karaiskos, L.

Sakelliou, E. Georgiou, and P. Papagiannis (2010). “Dosimetric accuracy

of a deterministic radiation transport based 192Ir brachytherapy treat-

ment planning system. Part I: single sources and bounded homogeneous

geometries.” Med Phys 37.2, pp. 649–661.

Zweit, J. (1996). “Radionuclides and carrier molecules for therapy”. Phys

Med Biol 41.10, pp. 1905–1914.

56

Errata

Publication IV

The caption in Figure 2. is truncated and the full caption should read as:

Regions of interest used to determine the biological clearance of the In-

111-labelled MoAb are shown. The body contours are taken on purpose

from another imaging to demonstrate that each imaging session may be

individual for body contour drawing.

57

Radiotherapy is an established treatment modality of cancer where radiation is delivered to the patients from internal or external sources. This thesis explores and introduces improvements to computational methods that are used in the application of internal and external radiotherapy. The summary discusses radiotherapy planning and reviews model-based dose calculation methods in internal and external radiotherapy. Treatment planning methods of internal radionuclide therapy are devloped and applied to analyze radionuclide therapy cases. The thesis also reports on the development of a pencil-beam dose kernel -based calculation method for external photon therapy that also accounts for local variations in tissue material densities in 3D space.

Aalto-D

D 57

/2016

9HSTFMG*aghchi+

ISBN 978-952-60-6727-8 (printed) ISBN 978-952-60-6728-5 (pdf) ISSN-L 1799-4934 ISSN 1799-4934 (printed) ISSN 1799-4942 (pdf) Aalto University School of Science Department of Neuroscience and Biomedical Engineering www.aalto.fi

BUSINESS + ECONOMY ART + DESIGN + ARCHITECTURE SCIENCE + TECHNOLOGY CROSSOVER DOCTORAL DISSERTATIONS

Joakim P

yyry C

onvolution and model-based dose calculation m

ethods in radionuclide and external-beam photon therapy

Aalto

Unive

rsity

2016

Department of Neuroscience and Biomedical Engineering

Convolution and model-based dose calculation methods in radionuclide and external-beam photon therapy

Joakim Pyyry

DOCTORAL DISSERTATIONS